Hypersequents and the Proof Theory of Intuitionistic Fuzzy Logic
Abstract
Takeuti and Titani have introduced and investigated a logic they called intuitionistic fuzzy logic. This logic is characterized as the first-order Goedel logic based on the truth value set [0,1]. The logic is known to be axiomatizable, but no deduction system amenable to proof-theoretic, and hence, computational treatment, has been known. Such a system is presented here, based on previous work on hypersequent calculi for propositional Goedel logics by Avron. It is shown that the system is sound and complete, and allows cut-elimination. A question by Takano regarding the eliminability of the Takeuti-Titani density rule is answered affirmatively.
Keywords
Cite
@article{arxiv.math/0005183,
title = {Hypersequents and the Proof Theory of Intuitionistic Fuzzy Logic},
author = {Matthias Baaz and Richard Zach},
journal= {arXiv preprint arXiv:math/0005183},
year = {2007}
}
Comments
v.2: 15 pages. Final version. (v.1: 15 pages. To appear in Computer Science Logic 2000 Proceedings.)